0. Hypothesis

0.1 Short rational

Temperature and enrichment are predicted to have dramatic impacts on food-webs
Stability is theoretically predicted to have an U-shape with stability (Uszko et al. 2017), higher temperature leading to higher stability in “cold” food-webs, and to lower stability in “hot” food-webs
Futhermore, metabolic theory predicts that higher trophic level suffer most from high temperature. Metabolic costs increase exponentially with temperature and higher trophic levels have generally higher body mass and then higher basal metabolic cost
Enrichment (measured here by DBO), is predicted to decrease stability by increasing the amplitude of population fluctuations (Rosenzweig 1971)
Insterestingly, enrichment is predicted to dampens the effect of high temperature by increasing resources thereby decreasing starvation risk due to high temperature (Tabi, Petchey, and Pennekamp 2019)
Stream and lakes are really different ecosystems:
- Stream fishes are highly contrained by stream flow
- Lakes are highly vertically stratified but offer limited opportunity for dispersal
- Streams are horizontal stratified and offer opportunity for dispersal
Develop hypothesis:
- about differences between lakes and streams…
- about the different network metrics

0.2 Methods

Network metrics: Connectance, Max trophic level, Mean trophic level, number of nodes
Environment: Temperature and DBO (to detail)

0.3 Statistical ideas

Simple linear model:

\(N_i = \alpha + \beta_0F + \beta_1T_i + \beta_2T_iF + \beta_3D_i + \beta_4D_iF + \beta_5D_iT_i \beta_6D_iT_iF+ \epsilon\)

With:
- \(i\): site i
- \(N_i\): Network metric of site \(i\)
- \(D\): DBO
- \(T\): Temperature
- \(F\): freshwater ecosystem type, lake or stream (logical variable ?)
- \(\alpha\): intercept
- \(\beta\): slope
- \(\beta_2\), \(\beta_4\), \(\beta_5\): slope of simple interaction
  - \(\beta_2\): link between network metrics and temperature change with ecosystem type ?
  - \(\beta_4\): link between network metrics and DBO change with ecosystem type ?
  - \(\beta_5\): link between network metrics and DBO change with temperature ? (hyp enrichment and temperature compensate each other)
- \(\beta_6\): slope of triple interaction; effect of temperature on the link between network metrics and DBO change with ecosystem type ?
Structural Equation Model (Gibert 2019):

DiagrammeR::grViz("digraph {
  graph [layout = dot, rankdir = TB]

  node [shape = rectangle]
  rec1 [label = 'Temperature']
  rec2 [label = 'DBO']
  rec3 [label =  'Species richness']
  rec4 [label = 'Number of nodes']
  rec5 [label = 'Mean trophic level']
  rec6 [label = 'Max trophic level']
  rec7 [label = 'Connectance']

  # edge definitions with the node IDs
  rec1 -> rec3
  rec1 -> rec4
  rec1 -> rec5
  rec1 -> rec6
  rec1 -> rec7

  rec2 -> rec3
  rec2 -> rec4
  rec2 -> rec5
  rec2 -> rec6
  rec2 -> rec7

  rec3 -> rec4
  rec3 -> rec5
  rec3 -> rec6
  rec3 -> rec7
  }",
  height = 500)

1. Temporal and spatial coverage

Due to biological and environmental data availability, the temporal coverage is from 2007 to 2016.
91 sampled lakes and 274 sampled stream stations were considered.

2. Environmental variables

	Lake					Stream
variable	mean	sd	median	min	max	mean	sd	median	min	max
dbo (mg/L)	1.5	0.9	1.3	0.5	5.5	1.6	0.6	1.5	0.6	4.9
temperature (°C)	13.9	1.9	13.6	9.6	18.5	11.3	1.9	11.3	1.8	17.8

3. Food web metrics

	Lake					Stream
metric	mean	sd	median	min	max	mean	sd	median	min	max
connectance	0.1	0.0	0.1	0.1	0.2	0.2	0.0	0.2	0.1	0.2
max trophic level	4.0	0.2	4.0	3.1	4.5	3.8	0.2	3.8	2.9	4.4
mean trophic level	3.3	0.2	3.3	2.2	4.0	3.5	0.3	3.5	2.7	4.2
number of nodes	40.8	10.2	39.0	21.0	67.0	31.4	14.8	30.0	8.0	92.0

4. Environmental variables vs. Food web metrics

References

Gibert, Jean P. 2019. “Temperature Directly and Indirectly Influences Food Web Structure.” Scientific Reports 9 (1): 5312. https://doi.org/10.1038/s41598-019-41783-0.

Rosenzweig, Michael L. 1971. “Paradox of Enrichment: Destabilization of Exploitation Ecosystems in Ecological Time.” Science 171 (3969): 385–87. https://doi.org/10.1126/science.171.3969.385.

Tabi, Andrea, Owen L. Petchey, and Frank Pennekamp. 2019. “Warming Reduces the Effects of Enrichment on Stability and Functioning Across Levels of Organisation in an Aquatic Microbial Ecosystem.” Edited by Tadashi Fukami. Ecology Letters 22 (7): 1061–71. https://doi.org/10.1111/ele.13262.

Uszko, Wojciech, Sebastian Diehl, Göran Englund, and Priyanga Amarasekare. 2017. “Effects of Warming on Predator-Prey Interactions - a Resource-Based Approach and a Theoretical Synthesis.” Edited by Ulrich Brose. Ecology Letters, March. https://doi.org/10.1111/ele.12755.

project_data_summary

Camille Leclerc

14/02/2022